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A chess problem is simply an exercise in pure mathematics.

G. H. Hardy

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G. H. Hardy
Age: 70 †
Born: 1877
Born: February 7
Died: 1947
Died: December 1
Academic
Mathematician
University Teacher
Cranleigh
Surrey
G. H. Hardy
Godfrey Harold Hardy
Godfrey·Harold·Hardy
Godfrey Harold
Chess
Mathematics
Exercise
Pure
Simply
Problem

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A science or an art may be said to be useful if its development increases, even indirectly, the material well-being and comfort of men, it promotes happiness, using that word in a crude and commonplace way.
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Greek mathematics is the real thing. The Greeks first spoke a language which modern mathematicians can understand... So Greek mathematics is 'permanent', more permanent even than Greek literature.
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Bombs are probably more merciful than bayonets
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The mathematician's patterns, like the painter's or the poet's, must be beautiful.
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The fact is there are few more popular subjects than mathematics. Most people have some appreciation of mathematics, just as most people can enjoy a pleasant tune.
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No mathematician should ever allow himself to forget that mathematics, more than any other art or science, is a young man's game
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A mathematician, like a painter or a poet, is a maker of patterns.
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A man who sets out to justify his existence and his activities has to distinguish two different questions. The first is whether the work which he does is worth doing and the second is why he does it (whatever its value may be).
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What we do may be small, but it has a certain character of permanence and to have produced anything of the slightest permanent interest, whether it be a copy of verses or a geometrical theorem, is to have done something utterly beyond the powers of the vast majority of men.
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Pure mathematics is on the whole distinctly more useful than applied... For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics.
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Mathematics is not a contemplative but a creative subject no one can draw much consolation from it when he has lost the power or the desire to create and that is apt to happen to a mathematician rather soon. It is a pity, but in that case he does not matter a great deal anyhow, and it would be silly to bother about him.
G. H. Hardy
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There is always more in one of Ramanujan's formulae than meets the eye, as anyone who sets to work to verify those which look the easiest will soon discover. In some the interest lies very deep, in others comparatively near the surface but there is not one which is not curious and entertaining.
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A science is said to be useful if its development tends to accentuate the existing inequalities in the distribution of wealth, or more directly promotes the destruction of human life.
G. H. Hardy
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Most people can do nothing at all well
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I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our creations, are simply the notes of our observations.
G. H. Hardy
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The public does not need to be convinced that there is something in mathematics.
G. H. Hardy
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If I could prove by logic that you would die in five minutes, I should be sorry you were going to die, but my sorrow would be very much mitigated by pleasure in the proof.
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Good work is not done by 'humble' men
G. H. Hardy
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No one has yet discovered any warlike purpose to be served by the theory of numbers or relativity, and it seems unlikely that anyone will do so for many years.
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I count Maxwell and Einstein, Eddington and Dirac, among real mathematicians. The great modern achievements of applied mathematics have been in relativity and quantum mechanics, and these subjects are at present at any rate, almost as useless as the theory of numbers.
G. H. Hardy